Splitting integrators for linear Vlasov equations with stochastic perturbations
Artikel i vetenskaplig tidskrift, 2024

We consider a class of linear Vlasov partial differential equations driven by Wiener noise. Different types of stochastic perturbations are treated: additive noise, multiplicative Itô and Stratonovich noise, and transport noise. We propose to employ splitting integrators for the temporal discretization of these stochastic partial differential equations. These integrators are designed in order to preserve qualitative properties of the exact solutions depending on the stochastic perturbation, such as preservation of norms or positivity of the solutions. We provide numerical experiments in order to illustrate the properties of the proposed integrators and investigate mean-square rates of convergence.

stochastic Vlasov equation

trace formula

positivity-preserving scheme

Stochastic partial differential equations

splitting scheme

preservation properties

Författare

Charles-Edouard Bréhier

David Cohen

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Journal of Computational Dynamics

2158-2505 (eISSN)

Vol. 11 4 494-532

Numerisk analys och simulering av PDE med slumpmässig dispersion

Vetenskapsrådet (VR) (2018-04443), 2019-01-01 -- 2022-12-31.

Ämneskategorier

Beräkningsmatematik

Reglerteknik

Matematisk analys

DOI

10.3934/jcd.2024014

Mer information

Senast uppdaterat

2024-09-18